Question

Assume a first estimate their price elasticity of demand (EQxPx) to be -3.5, and their marginal cost to be $15.

3. Assume a firm estimate their price elasticity of demand (EQxPx) to be -3.5, and their marginal cost to be $15. a. Using the mark-up rule, what is the optimal price for the firm to charge? 2 points b. Confirm that your answer above is correct, by computing the profit maximizing quantity and price using MR = MC if the firm's inverse demand function is Px - 27 -0.25Qx and MC - $15. 2 points c. What is the defining feature of a Pure Selling Problem? 1 point

Answer 1

1. As a rule of thumb, the monopolist should charge the optimal price using the markup formula

P= MC/(1+1/E_d)

where P is price, MC is marginal cost and E_d is elasticity of demand.

Putting values given MC= $ 15 and E_d = -3.5 in the formula

P= 15/(1+1/-3.5) P=15(0.72)

=$20.9 approx

2. To compute the profit maximising output and price, we need MR i.e Marginal Revenue

To calculate MR, we need Total Revenue first

so TR= Price*Quantity

we have the inverse demand function as P_x = 27-.0.25Qx

so TR= 27-.0.25Qx * Q

TR= 27Q-0.25Qx²

We will get MR by differentiating TR, Hence MR= 27-0.50Qx

Putting MR=MC

27-0.50Qx=15

Optimal Quantity (Q)= 24 units

Getting optimal price= Px= 27-0.25(24)

Px= $21

Hence, the first answer is verified.

3. The defining feature if a pure selling problem is that Marginal cost is zero.