Answer to Question #271518 in Microeconomics for lilia

Question

Consider two digital startups S and T. Following information about fixed and marginal cost in the short run is available: • Fixed cost FCS = 5000; constant marginal cost MCS = 40, • Fixed cost FCT = 100; marginal cost MCT = 10Q, where Q is the quantity of output produced.

a) State both startup’s total cost function !

b) What are the average cost AC(Q) of the two firms ?

c) Suppose government imposes a digital tax of 0.5 per unit of output. How does this tax affectmarginal, averageandtotalcost? Ifgovernmentchargedalump(fixed)sum,which cost would be affected ?

d) Suppose the startups are successful and stay in the market. Would you expect long run average cost to smaller or larger than average cost in the short run ? Briefly explain.

e) Can you say something about long run marginal cost, if you know that long run average cost is constant ? Does this imply anything with regard to returns to scale ? Briefly explain.

Answer 1

(a)

start up S:

$FC=5000$

$MC=40$

$TC=40Q +5000$

start up T:

$FC=100$

$MC=10Q$

$TC=5Q^2 +100$

(b)

$AC=\frac{TC}{Q}$

start up S:

$AC=\frac{40Q+5000}{Q}$

$AC=40+\frac{5000}{Q}$

start up T:

$AC=\frac{5Q^2+100}{Q}$

$AC=5Q+\frac{100}{Q}$ .

(c)

A per unit tax increases a firm's marginal cost and average variable cost and thus, also the average total cost. A per unit tax will likely cause a firm to reduce its output in the short run, since marginal cost shifts up and moves along the demand curve.

If the government charged a lump sum, only the average total cost will be affected because the firm's average fixed cost will increase.

(d)

The long run average cost would be smaller than the short run average cost. This is because there are no fixed factors in the long run and thus there exist no fixed costs.

(e)

If the long run average cost is constant, this implies that marginal cost will be equal to the average cost, since the average cost curve reaches its lowest point. There will be zero fixed costs and constant marginal cost.

This implies that there will be constant returns to scale because the average cost does not change as output increases.