Question

In: Economics

ACME Manufacturing monopolizes the market for lava lamps. Demand for lava lamps is described by the inverse demand curve, P = 148 − 2Q. ACME’s total costs are given by C(Q) = 10 + 4Q

ACME Manufacturing monopolizes the market for lava lamps. Demand for lava lamps is described by the inverse demand curve, P = 148 − 2Q. ACME’s total costs are given by C(Q) = 10 + 4Q.

1. What is ACME’s marginal cost?

2. What are ACME’s total profits as a function of Q only? (i.e., what is π(Q)?)

3. Write down ACME’s profit maximization problem assuming it chooses what quantity to produce.

4. Find an equation which must hold if ACME is maximizing profits.

5. Find the optimal quantity of lava lamps for ACME to produce.

6. If ACME produces lamps at its profit maximizing quantity, what is the price of a lava lamp?

7. If ACME is maximizing profits, what profit does it receive?

Expert Solution

1. MC = dTC/dQ = 4

2. Profit(Q) = PQ - TC = (148Q-2Q²) - (10+4Q) = 144Q - 2Q² - 10

3. Max. PQ s.t. TC

That is,

Maximize 148Q - 2Q² with respect to 10+4Q

4. Condition to hold true to maximize profits

MR = MC

148 - 4Q = 4

5. At the optimal point, P = MC

That is, P = 4

Substitute this in the demand function,

P = 148-2Q

4 = 148-2Q

Q* = 72 units

6. Profits are maximized where MR = MC

This makes,

148-4Q = 4

Q' = 36 units

P' = $76

7. Profit = TR-TC

Profit = PQ - TC

Profit = (76*36) - (10+4*36)

Profit = $2582

Rahul Sunny answered 2 years ago

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