Question

suppose a firm faces a demand function Q= 400-2P

3. (20 points) Suppose a firm faces a demand function 0 = 400 - 2P. Costs are C = 138 + 200. (a) Set up the revenue function R. (b) Find Q and P that maximize profit. (c) Suppose fixed costs increase to 200. Show (with math) how this change affects the profit maxi- mizing solution. Who bears the increase in cost? (d) Suppose variable costs increase to 40. Show (with math) how this change affects the profit max- imizing solution. Who bears the increase in cost?

Answer 1

The important thing is to make sure that you convert the demand function into inverse demand function. Which means price as a function of quantity and quantity is an independent variable because the firm's cost function is a function of quantity.

PAGE Ta Demand turretion, 400-21 we need to find the inverse derrand function, that is Derrand in which Price is a function of Quantity. Because the tirm len only choose the wantity if produces not the price. 292 400-Q L P = 200- 0/2 Revenue a Price x Quantity R (200-0/2) XQ O b) Profit of firm, denoted by ñ [ a Revenue - lost a I lost furretion of firm b 138 + 200 T2 (200-a) xo - ( 138 +200) To maximize profif we use tilf order Condition di za da dyra die 1200-2)[7) - 10 - 200-8-20 da

az 200-20 Q 2 180 inverse demand 02180 in turabilm we get P2 110 (c) If - the fixed lost lost turition Increases to 200 for firm becomes (z 200+ 200 - Again Protif meximizing condition II (Wooajxu - 1200+200). 1 2 (200-0)7-12a - 20 200-a-2020 az 180 and P2 20-180 220-90 Pello

As we can see when the fixed cost of form increases to 200 the equilibrium price and quantity doesn't change which means all the cost is beared by the firm. Because fixed cost as sunk cost that is it is the cost that firm bears at 0 level of production. So fixed cost is always beared by the firm.

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- DATI PAGR ( when variable lost for form Increases to yo. The lost furretion for firm becomes L 138+ YOQ Again Proff maximizing condition, T R-1 T2 (200 - Q xa - ( 138 +408) dir - (200-2) 13e - 40 - dil to dQ o = 200-Q -yo Q- 160 Pulting Q²160 info Inverse cerrand funktion we get Pa 200-80 P2 120

When the variable cost increases to 40 per unit. The equilibrium price increases by 10 per unit which means both consumers and producers bear the burden of increased cost.