Question

Ron's Window Washing Service is a small business that operates in the perfectly competitive residential window washing industry in Evanston, Illinois. The short-run total cost of production is STC(Q) = 40+ 100 + 0.1Q?, where Q is the number of windows washed per day. The corresponding short-run marginal cost function is SMC(q) = 10 + 0.29. The prevailing market price is $20 per window. a) How many windows should Ron wash to maximize profit? b) What is Ron's maximum daily profit? c) Graph SMC, SAC, and the profit-maximizing quantity. On this graph, indicate the maximum daily profit. d) What is Ron's short-run supply curve, assuming that all of the $40 per day fixed costs are sunk? e) What is Ron's short-run supply curve, assuming that if he produces zero output, he can rent or sell his fixed assets and therefore avoid all his fixed costs?

Answer 1

a. total profit = total revenue-total cost

at maximum profit, marginal cosst=marginal revenue

hence, 20=smc as 20 is the price=marginal revenue

hence,10+0.2Q=20 or 0.2Q=10 or Q=50

hence he has to produce 50 windows to maximum profit.

b. at Q=50 his total revenue=pricex50=20x50=1000

nd total cost=40+10x50+0.1x50²=790

hence total profit at Q=50 is 1000-790=210

c.

the black shaded area is the profit.

50 is the profit maximising quantity.

060 08 OL 09 Os OP 0€ OC OL TTUS SAC mc price and Cost

d. the short-run supply curve of the firm is the portion of MC for which P>=AVC

hence, AVC=TVC/Q=10+0.1Q (as 40 is the fixed cost)

hence when P>=10+0.1Q

or, 20>=10+0.1Q

or, 10>=0.1Q

hence Q<=100

hence the part of MC when Q is not greater than 100 is the short-run supply curve of the firm.

e. if this is the case hence the whole cost will be a variable cost function,

hence AVC will be 40/Q+10+0.1Q

and the supply condition will be, 20>=40/Q=10+0.1Q

or, 200Q>=400+100Q+Q² or Q²-100Q+400<=0

or (Q-95.82)(Q-4.17)<=0

hence when Q-95.82>=0 or Q>95.82 then ( Q-4.17)<=0 or Q<4.17 this cannot be true at the same time

or otherwise Q>=4.17 and Q<=95.82 but this is valid.

hence the supply curve will be the part of MC where Q is between 4.17 and 95.82.