The demand function for a product using resource X is given by Q = 180-2P and th

Question

The demand function for a product using resource X is given by Q = 180-2P and the cost of production is constant at MC = 20

1. Write the inverse demand function for this product

2. Find the static equilibrium for this product in a single time period (call this t­­­­­0)

3. Write the function for Marginal Net Benefit (MNB) (Hint: Because MC is constant, simply subtract MC from the inverse demand curve to establish MNB)

4. Suppose that there is a limited stock amount of 200 units that can be consumed in two time periods t0 and t1. Assume that the current generation (those consuming in t0) pay no regard at all to the consumption in t1. How much is left to consume in t1?

5. Suppose the discount rate is 4%. What is the dynamically efficient consumption/production in t0? What is the dynamically efficient consumption/production in t1?

6 When future benefits are discounted, is the dynamically efficient consumption of the current generation higher or lower than that which occurs without discounting? Explain why.

Explanation / Answer

1. Demand function Q = 180-2P

Inverse demand function => 2P = 180- Q

=> P = 90 - Q/2

2. Static equilibrium is obtained where MR = MC

TR = PQ = 90Q - Q2/2

MR = 90 - Q (differentiating TR with respect to Q)

MR = MC => 90- Q = 20

Hence, Q = 70.

P = 90- 70/2 = 90- 35= 55

3. Marginal net benefit (MNB) function = Inverse demand function - MC

MNB = 90- Q/2 - 20 = 70- Q/2

4. Equilibrium quantity in t0 period is 70 units according to the demand function. Therefore, among 200 units, 200- 70 = 130 units are left for the consumption in t1.

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