Integrating problem The manager of the Electronic Corporation has estimated the

Question

Integrating problem The manager of the Electronic Corporation has estimated the total variable costs and the total fixed cost functions for producing a particular type of camera to be TVC = 60Q-12Q2 + Q3 TFC = $100 The corporation sells the cameras at the price of $60 each An engineering study just published estimated that if the corporation employs newly developed technology, the long-run total cost function would be TC = 50+20Q+2w+3r where w = wage rate and r = rental price of capital The manager asks you to find. The average variable and marginal cost functions of the firm, the output level at which the two curves cross, and a plot of them The breakeven output of the firm and the output at which the firm maximizes its total profits; The long-run average cost and long-run marginal cost functions with the new technology if w = $20 and r = $10. and plot them. Are these curves similar to those found in other empirical studies of the long-run costs? Should the corporation adopt the new technology? If it did, what would be the profit-maximizing level of output if the firm can continue to sell its cameras at the price of $60 per unit Instruction: Please Do Not Handwrite The Answers. Typed Answers Will Be Appreciated.

Explanation / Answer

a)

TVC=60Q-12Q^2+Q^3

TC=TVC+FC

TC=100+60Q-12Q^2+Q^3

Average variable cost=TVC/Q=(60Q-12Q^2+Q^3)/Q

Average variable cost Function=60-12Q+Q^2

Marginal cost=d(TC)/dQ = d(100+60Q-12Q^2+Q^3)/dQ

Marginal cost function=60-24Q+3Q^2

b)

For the Profit maximization

MC=MR

MR=$60

MC=60-24Q+3Q^2

For the Profit maximization

60=60-24Q+3Q^2

3Q^2=24Q

Q^2=14/3=8

Q=2.82

Thus breakeven output=2.82 unit =3 unit approx.

c)

For Long run TC=50+20Q+2w+3r

For w=20,r=10

TC=50+20Q+2*20+3*10=130+20Q

Average cost=TC/Q=(130+20Q)/Q=130/Q+20

Marginal cost=d(TC)/dQ

Marginal cost=d(130+20Q)/dQ=20

In long run all there is no fixed cost, all cost like: labor, capital is variable

The Equation for long run Total Cost function has both wages and capital variable. Thus the curve is similar to th those found in other empirical studies of the long run cost

d)

Yes the corporation should adopt the new technology as the marginal cost is less in the new technology

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