Answer the following questions. The solutions will be provided in the lab sessio

Question

Answer the following questions. The solutions will be provided in the lab sessions on November 13 and 15. 1. The short run cost function of a firm is given by TC=200 + 55g, where TC is the total cost and g is the quantity of output produced. ) What is the firm's fixed cost? (ii) If the firm produces q = 100, what would be its average fixed cost, average variable ocst, and marginal cost of production? 2. The production function of a frin is given by q 5KL, where q denotes the uantity of output produced and K and L denote capital and labour used. For this production function, the marginal product of labour is MR, 5K, and the marginal product of capital is MPK-5L-The wage rate is w = 5000 and the rental rate is r 10000, Suppose in the short run the firm's capital is fixed at K-4. (6) Derive the short run total cost function of this firm (ie. express short run total cost as a function of q). (i) In the short run, how many units of L is needed to produce q-2507 i) What is the total cost of producing 250 in the short run? (iv) In the long run, what is the capital-to-labour ratio that minimizes the pro- duction cost of this firm? (v) In the long run, how many units of L and K should this firm use in order to produce 9-250 in a cost-minimizing manner? (vi) what is the total cost of producing q = 250 in the long run?

Explanation / Answer

Question 1

(i)

Total cost function is as follows -

TC = 200 + 55q

The constant part of total cost function represents firm's fixed cost.

So, the firm's fixed cost is $200.

(ii)

Total fixed cost, TFC = 200

Output produced, q = 100

Calculate the average fixed cost -

AFC = TFC/q = 200/100 = 2

The average fixed cost is $2.

TC = 200 + 55q

The constant part represents fixed cost while remaining part represents variable cost.

So,

TVC = 55q

Output produced, q = 100

TVC = 55* 100 = $5,500

Calculate average variable cost -

AVC = TVC/q = 5,500/100 = 55

The average variable cost is $55.

Calculate the marginal cost -

TC = 200 + 55q

MC = dTC/dQ = d(200+55q)/dq = 55

The marginal cost of production is $55.

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