Suppose that a price-setting firm has the following total revenue and total cost

Question

Suppose that a price-setting firm has the following total revenue and total cost functions: R(q) = 10.75q _ 0.18759" and C(q) 75+ 0.07q + 0.035q' . of 893 This firm faces downward sloping demand and marginal revenue curves. Marginal revenue and marginal cost are given by MR(q) 10.75-0.375q and MC(q)= 0.07 + 0.07q respectively a. Using the marginal revenue function given above, find an expression for the firm's demand curve as a function of q. Le, Dlq) -p-27 w hat is the firm's profit maximizing output level? C(q) b. Le.. MAX wrt q: (q)-R(q)- c. Since the firm is a price setter, rather than a price taker, what price will it need to set in order to achieve the profit maximizing output level from b. above? Using the answers you found in b. and c. above, what is the firm's total revenue? d. e. Using the results you found above, find the firm's inverse demand function. Le, D(p f. Using the results you found from b, c, and e. above, what is the price elasticity of demand (ie, (p/q)-(Aq/Ap) ) at the firm's profit maximizing output level? Is the profit maximizing output level in the elastic range or is it the inelastic range of the firm's demand curve? g. Use the open source "Graph" software (version 4.4.2 downloadable at D to plot the total revenue function, the cost function and the Print copies of your graphs and attach thern to this exam other graphing software, profit ( TR-TC) function. or email them to such as https://ww Page 3 6 or use it r

Explanation / Answer

Ans 1) a) Price=2 is shut down point because P=min of AVC

B)P should be atleast 3 to get economic profit

C)when P=4, 36000 units of Q should be produced and profit=(4-3)*36000=36000

D)draw a horizontal line at 2.5 i.e. Parallel to x axis.

E)when P=2 Then Q=30000

F)when P=1.5 firm will shut down and Q=0

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