Questions: The market demand and supply curves in a perfectly competitive industry are given by: Pd=28-Q / 750 and Ps=-20+Q / 250. Complete the following questions. a) Draw these functions on the graph below. b) Calculate the equilibrium price and output in this industry. Equilibrium price = 0 Equilibrium output = 0 c) Now assume that an additional firm is considering entering. This firm has a short run MC curve defined by MC=8+0.5 q, where q is the firm's output. If this firm enters the industry, what output should it produce? (Hint: It will set P = MC.) Output = 0

Solution Steps

• The demand function is given by \( P_d = 28 - \frac{Q}{750} \).
• The supply function is given by \( P_s = 20 + \frac{Q}{250} \).

To draw these functions:

1. For the demand curve, set \( Q = 0 \) to find the intercept: \( P_d = 28 \).
2. For the supply curve, set \( Q = 0 \) to find the intercept: \( P_s = 20 \).
3. Find another point for each curve by setting \( P = 0 \) and solving for \( Q \).

• At equilibrium, \( P_d = P_s \).

Set the demand and supply equations equal to each other: \[ 28 - \frac{Q}{750} = 20 + \frac{Q}{250} \]

Solve for \( Q \): \[ 28 - 20 = \frac{Q}{250} + \frac{Q}{750} \] \[ 8 = \frac{4Q}{750} \] \[ 8 = \frac{2Q}{375} \] \[ 8 = \frac{Q}{187.5} \] \[ Q = 8 \times 187.5 \] \[ Q = 1500 \]

Substitute \( Q = 1500 \) back into either the demand or supply equation to find \( P \): \[ P = 28 - \frac{1500}{750} \] \[ P = 28 - 2 \] \[ P = 26 \]

• The new firm's marginal cost (MC) curve is given by \( MC = 8 + 0.5q \).
• In a perfectly competitive market, the firm will produce where \( P = MC \).

Set \( P = 26 \) equal to the MC equation: \[ 26 = 8 + 0.5q \]

Solve for \( q \): \[ 26 - 8 = 0.5q \] \[ 18 = 0.5q \] \[ q = \frac{18}{0.5} \] \[ q = 36 \]

Final Answer