The price rose ten percent and the revenue fell

# Self-authored for the EML case corpus (no external origin). A seller raises its
# price by ten percent to raise revenue, the increase is applied exactly, and the
# revenue afterwards is measured exactly. What revenue is a product of is
# computed below.
#
# The move is careful. The new price is exactly ten percent above the old; every
# sale is at the new price; the revenue before and after is real; and the intent
# is exactly 'more revenue'.
#
# Revenue is price times quantity, and quantity fell fifteen percent when price
# rose ten - the demand was elastic - so the exact ten-percent rise produced an
# exact revenue fall.

10 => price_before
1000 => units_before
11 => price_after
850 => units_after
9 => price_if_cut
1150 => units_if_cut

price_before * units_before => revenue_before
price_after * units_after => revenue_after
revenue_after - revenue_before => revenue_change
int((price_after - price_before) * 10000 / price_before) => price_rise_per_myriad
int((units_before - units_after) * 10000 / units_before) => units_fall_per_myriad
int(units_fall_per_myriad * 100 / price_rise_per_myriad) => elasticity_hundredths
price_if_cut * units_if_cut => revenue_if_cut
revenue_if_cut - revenue_before => revenue_change_if_cut

"price before / after            : " + str(price_before) + " / " + str(price_after) + ", up " + str(price_rise_per_myriad) + " per ten thousand" ^0
"units before / after            : " + str(units_before) + " / " + str(units_after) + ", down " + str(units_fall_per_myriad) + " per ten thousand" ^0
"" ^0
"revenue before                  : " + str(revenue_before) ^0
"revenue after the rise          : " + str(revenue_after) ^0
"revenue change                  : " + str(revenue_change) ^0
"elasticity                      : " + str(elasticity_hundredths) + " hundredths, above one" ^0
"" ^0
"had the price been cut to " + str(price_if_cut) + "    : " + str(units_if_cut) + " units, revenue " + str(revenue_if_cut) + ", change " + str(revenue_change_if_cut) ^0
"" ^0

# ---- what the move verified ----

"the price rise" ^0
"  new price : exactly ten percent above the old" ^0
"  sales : every one at the new price" ^0
"  revenue : real before and after" ^0
"  intent : more revenue" ^0
"  sales at the old price after the rise : 0" ^0
"  verdict : THE PRICE WENT UP TEN PERCENT, EXACTLY" ^0
"" ^0
"  applying the rise exactly to every sale is the part done" ^0
"  right here, and it is why the price side of the move is" ^0
"  precisely what was intended" ^0
"" ^0

# ---- what revenue is a product of ----

"price times quantity" ^0
"  what revenue is : price times units, not price" ^0
"  what the rise did to units : " + str(units_before) + " to " + str(units_after) + ", down " + str(units_fall_per_myriad) + " per" ^0
"    ten thousand" ^0
"  the ratio of the two moves : " + str(elasticity_hundredths) + " hundredths, so units fell" ^0
"    faster than price rose" ^0
"  so revenue : " + str(revenue_before) + " to " + str(revenue_after) ^0
"  the direction that would have raised it : a cut, to " + str(revenue_if_cut) ^0
"" ^0

# ---- what the seller got ----

"the quarter" ^0
"  revenue change from the rise : " + str(revenue_change) ^0
"  revenue change a cut would have made : " + str(revenue_change_if_cut) ^0
"  is the price rise misapplied : no; it is exactly ten" ^0
"    percent" ^0
"  is a higher price more revenue : only when demand moves" ^0
"    less than price, and here it moved more" ^0
"" ^0

# ---- null control ----

# The same seller estimating the elasticity first (a small test in each
# direction) and moving price the way that raises price times quantity.
revenue_after - revenue_before => nc_revenue_change_moving_price_up
350 => nc_revenue_change_moving_price_down
1 => nc_direction_chosen_by_elasticity_is_down

"null control - measure the elasticity, then choose the direction" ^0
"  revenue change, price up : " + str(nc_revenue_change_moving_price_up) ^0
"  revenue change, price down : " + str(nc_revenue_change_moving_price_down) ^0
"  direction chosen by the elasticity is down : " + str(nc_direction_chosen_by_elasticity_is_down) ^0
"  no customer and no cost changed; price stopped being" ^0
"  moved as if quantity would stand still" ^0
"" ^0

# ---- the rule ----

"what an exact ten-percent price rise guarantees" ^0
"  every sale brings in ten percent more than before :" ^0
"    exactly, the rise applied to every sale" ^0
"  revenue rises : not addressed; units fell " + str(units_fall_per_myriad) + " per ten" ^0
"    thousand against a " + str(price_rise_per_myriad) + " rise in price, so price times units" ^0
"    fell from " + str(revenue_before) + " to " + str(revenue_after) ^0
"" ^0

"a revenue is a product, and moving one factor moves the other; when the" ^0
"quantity answers by more than the price asked, the exact rise on every sale is" ^0
"an exact fall on the total, and the lever was pushed the wrong way" ^0
"" ^0

"It raises the price by exactly ten percent on every sale - the price side is" ^0
"precise. But units fell " + str(units_fall_per_myriad) + " per ten thousand, an elasticity of " + str(elasticity_hundredths) + " hundredths, so" ^0
"revenue went from " + str(revenue_before) + " to " + str(revenue_after) + ", " + str(revenue_change) + ", where a cut to " + str(price_if_cut) + " would have made" ^0
"" + str(revenue_change_if_cut) + ", until the elasticity was measured before the lever was pulled." ^0

price_before = 10
units_before = 1000
price_after = 11
units_after = 850
price_if_cut = 9
units_if_cut = 1150
revenue_before = price_before * units_before
revenue_after = price_after * units_after
revenue_change = revenue_after - revenue_before
price_rise_per_myriad = int((price_after - price_before) * 10000 / price_before)
units_fall_per_myriad = int((units_before - units_after) * 10000 / units_before)
elasticity_hundredths = int(units_fall_per_myriad * 100 / price_rise_per_myriad)
revenue_if_cut = price_if_cut * units_if_cut
revenue_change_if_cut = revenue_if_cut - revenue_before
print("price before / after            : " + str(price_before) + " / " + str(price_after) + ", up " + str(price_rise_per_myriad) + " per ten thousand")
print("units before / after            : " + str(units_before) + " / " + str(units_after) + ", down " + str(units_fall_per_myriad) + " per ten thousand")
print("")
print("revenue before                  : " + str(revenue_before))
print("revenue after the rise          : " + str(revenue_after))
print("revenue change                  : " + str(revenue_change))
print("elasticity                      : " + str(elasticity_hundredths) + " hundredths, above one")
print("")
print("had the price been cut to " + str(price_if_cut) + "    : " + str(units_if_cut) + " units, revenue " + str(revenue_if_cut) + ", change " + str(revenue_change_if_cut))
print("")
print("the price rise")
print("  new price : exactly ten percent above the old")
print("  sales : every one at the new price")
print("  revenue : real before and after")
print("  intent : more revenue")
print("  sales at the old price after the rise : 0")
print("  verdict : THE PRICE WENT UP TEN PERCENT, EXACTLY")
print("")
print("  applying the rise exactly to every sale is the part done")
print("  right here, and it is why the price side of the move is")
print("  precisely what was intended")
print("")
print("price times quantity")
print("  what revenue is : price times units, not price")
print("  what the rise did to units : " + str(units_before) + " to " + str(units_after) + ", down " + str(units_fall_per_myriad) + " per")
print("    ten thousand")
print("  the ratio of the two moves : " + str(elasticity_hundredths) + " hundredths, so units fell")
print("    faster than price rose")
print("  so revenue : " + str(revenue_before) + " to " + str(revenue_after))
print("  the direction that would have raised it : a cut, to " + str(revenue_if_cut))
print("")
print("the quarter")
print("  revenue change from the rise : " + str(revenue_change))
print("  revenue change a cut would have made : " + str(revenue_change_if_cut))
print("  is the price rise misapplied : no; it is exactly ten")
print("    percent")
print("  is a higher price more revenue : only when demand moves")
print("    less than price, and here it moved more")
print("")
nc_revenue_change_moving_price_up = revenue_after - revenue_before
nc_revenue_change_moving_price_down = 350
nc_direction_chosen_by_elasticity_is_down = 1
print("null control - measure the elasticity, then choose the direction")
print("  revenue change, price up : " + str(nc_revenue_change_moving_price_up))
print("  revenue change, price down : " + str(nc_revenue_change_moving_price_down))
print("  direction chosen by the elasticity is down : " + str(nc_direction_chosen_by_elasticity_is_down))
print("  no customer and no cost changed; price stopped being")
print("  moved as if quantity would stand still")
print("")
print("what an exact ten-percent price rise guarantees")
print("  every sale brings in ten percent more than before :")
print("    exactly, the rise applied to every sale")
print("  revenue rises : not addressed; units fell " + str(units_fall_per_myriad) + " per ten")
print("    thousand against a " + str(price_rise_per_myriad) + " rise in price, so price times units")
print("    fell from " + str(revenue_before) + " to " + str(revenue_after))
print("")
print("a revenue is a product, and moving one factor moves the other; when the")
print("quantity answers by more than the price asked, the exact rise on every sale is")
print("an exact fall on the total, and the lever was pushed the wrong way")
print("")
print("It raises the price by exactly ten percent on every sale - the price side is")
print("precise. But units fell " + str(units_fall_per_myriad) + " per ten thousand, an elasticity of " + str(elasticity_hundredths) + " hundredths, so")
print("revenue went from " + str(revenue_before) + " to " + str(revenue_after) + ", " + str(revenue_change) + ", where a cut to " + str(price_if_cut) + " would have made")
print("" + str(revenue_change_if_cut) + ", until the elasticity was measured before the lever was pulled.")

price before / after            : 10 / 11, up 1000 per ten thousand
units before / after            : 1000 / 850, down 1500 per ten thousand

revenue before                  : 10000
revenue after the rise          : 9350
revenue change                  : -650
elasticity                      : 150 hundredths, above one

had the price been cut to 9    : 1150 units, revenue 10350, change 350

the price rise
  new price : exactly ten percent above the old
  sales : every one at the new price
  revenue : real before and after
  intent : more revenue
  sales at the old price after the rise : 0
  verdict : THE PRICE WENT UP TEN PERCENT, EXACTLY

  applying the rise exactly to every sale is the part done
  right here, and it is why the price side of the move is
  precisely what was intended

price times quantity
  what revenue is : price times units, not price
  what the rise did to units : 1000 to 850, down 1500 per
    ten thousand
  the ratio of the two moves : 150 hundredths, so units fell
    faster than price rose
  so revenue : 10000 to 9350
  the direction that would have raised it : a cut, to 10350

the quarter
  revenue change from the rise : -650
  revenue change a cut would have made : 350
  is the price rise misapplied : no; it is exactly ten
    percent
  is a higher price more revenue : only when demand moves
    less than price, and here it moved more

null control - measure the elasticity, then choose the direction
  revenue change, price up : -650
  revenue change, price down : 350
  direction chosen by the elasticity is down : 1
  no customer and no cost changed; price stopped being
  moved as if quantity would stand still

what an exact ten-percent price rise guarantees
  every sale brings in ten percent more than before :
    exactly, the rise applied to every sale
  revenue rises : not addressed; units fell 1500 per ten
    thousand against a 1000 rise in price, so price times units
    fell from 10000 to 9350

a revenue is a product, and moving one factor moves the other; when the
quantity answers by more than the price asked, the exact rise on every sale is
an exact fall on the total, and the lever was pushed the wrong way

It raises the price by exactly ten percent on every sale - the price side is
precise. But units fell 1500 per ten thousand, an elasticity of 150 hundredths, so
revenue went from 10000 to 9350, -650, where a cut to 9 would have made
350, until the elasticity was measured before the lever was pulled.

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