Final exam 21 January 2021, answers PDF

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Ans to Ques No -1 a) the difference between short run and long run are explained below: Short run -period of time in which at least one factor of production remains fixed. Generally, capital remain fixed. Output increase by labor. (variable input) Long run -period of time during which all inputs are variable inputs. It may increase labor or capital input. b) Cobb -douglas production function, Q = 10 √K √L Marginal product of capital MPK = (dQ/dK) = 10 (1/2) (√L/√K) =5 (L0.5/K0.5) Marginal product of labor MPL = (dQ/dL) = 10 (1/2)(√K/√L) =5 (K0.5 /L0.5 ) c) The law states that when increasing amount of the variable inputs are combined with a fixed level of another input, a point will be reached where the marginal product of the variable input will decline. MPL = (∆Q/∆L) Here, ∆L =change in output when labor is increased by 1 unit. MPL = marginal product of labor If MPL is very small then MPL = dQ/dL d)Total product of labor is (TPL) .It is equal to the production function and shows total output (Q) in the short run given the variable input, holding capital constant. Average Product of Labor (APL) equals Q/L while Marginal Product of Labor (MPL) equals the extra output gained by hiring one more unit of labor

Ans to Ques No – 2 a) Assuming the capital is fixed a firm will determine the optimal employment of labor in the following way – Additional units of the variable output should be hired until the marginal revenue product (MRP) of the last unit employed is equal to the cost of the input. The MRP is defined as marginal revenue times marginal product and represents the value of the extra unit of labor. In general, MRP = MRxMP P =MR (price =constant) ( mkt is perfectly competitive) MRPL =MR X MPL Thus, labor is hired until MRPL equals the wage rate (w) MRPL = w b) Production functions Q = 2√K √L MPL =dQ/dL = 2 (1/2) (√K/√L) = √K /√L capital stock (K= 16) units is fixed price of output Q =$5 wage rate w =$3 here MRPL =P x MPL = 5 ( 160.5 /L0.5 ) = 20 /√L Again MRPL = w 20/√L =3 Or 400/ L = 9 Or 9L = 400

L = 44.44 Therefore 44.44 units of labor should be employed which is the optimal rate. Ans to Ques No -3 a) i) Isoquant : An isoquant is derived from the production function which shows all combinations of labor and capital that will produce a given rate of output. ii) The slope of an isoquant gives the marginal rate of technical substitution (MRTS) .It means the increase in the quantity of one factor that is required to replace a unit decrease in another factor, when output is held constant along any isoquant. Slope of an isoquant (MRTS) is equal to the negative of the ration of the marginal product that is MRTS = -(MPL/MPK) (iii) The shape of this isoquant implies that inputs are imperfectly substitutable and the rate of substitution declines as one input is substituted for another. If it was perfectly substitutable then the line will be straight. The shape of the isoquants shows the rate at which one input can be substituted for the other such that the level of output remains constant. b) i) Production isocost - The isoquant is a physical relationship that denotes different ways to produce a given rate of output. The next step toward determining the optimal combination of capital and labor is to add information on the cost of those inputs. This cost information is introduced by a function called a production isocost. ii) the equation of isocost line – let the per unit prices of capital(r) and labor(w) the total expenditure (C) on capital and labor input is C = rK + wL iii) We know , C =rK+wL 40 = 3K+5L [ r= 3] K = (40/3) +(40/5) L =13.33 + 8L

Similarly 40 =4K+5L

[r=4]

K =10 +8L Here the budget constrained remains fixed. Since the labor(r) is increasing the isocost line is getting steeper.

Ans to Ques No -4 4. Explain how: (a) a firm minimizes cost of a given rate of output; and (b) a firm maximizes output given a budget constraint. a) A firm minimizes cost of a given rate of output given a budget constraint let the firm’s main objective is to minimize the cost of a given rate of output. The firm need to choose the absolute minimum cost combination of capital and labor. That is , the marginal rate of substitution equals the price of labor divided by the price of capital . MRTS = w/r b) A firm maximizes output given a budget constraint The objective is to maximize output given a budget constraint. the firm need to choose the point where the higher rate of output is produced. The optimal point is, the isoquant is tangent to the isocost. Hence the same efficiency condition MRTS =W/(r ) applies

Ans to Ques No -5 TC = 2000 +20Q -3Q2 +4Q3 Here d(TC)/dQ =MC = 20 -6Q +12Q2 Now we find the TVC by subtracting the FC component from the total cost component TVC = 20 Q -3Q2 +4Q3 AVC =

TVC Q

2 3 = 20 Q−3Q + 4 Q =20 −3Q+ 4 Q2

Q

Again AVC =MC 20 -3Q+4Q2 =20 -6Q+12 Q2 Or 3Q -8Q2 = 0 Or Q(3 -8Q) = 0 Which has the roots of Q = 0 or 3-8Q =0 Or Q = (3/8) The rate of output Q =(3/8) units which will result in minimum average variable cost....