Economics

Question 1 A firm faces the following total product curves depending on how much capital it employs: K = 1 unit | K = 2 units | K = 3 units | Quantity of Labor | Total Product | Quantity of Labor | Total Product | Quantity of Labor | Total Product | 1 | 100 | 1 | 123 | 1 | 139 | 2 | 152 | 2 | 187 | 2 | 193 | 3 | 193 | 3 | 237 | 3 | 263 | 4 | 215 | 4 | 263 | 4 | 319 | 5 | 233 | 5 | 286 | 5 | 366 | 6 | 249 | 6 | 306 | 6 | 407 | 7 | 263 | 7 | 323 | 7 | 410 | a. Suppose that the firm currently employs 1 unit of capital and 3 of labor. Compute MRTSLK. Compute MPL. Compute MPK. [3 marks] Computation of MPL and MPK will be performed first prior to MRTSLK. Computation of MPL can be done using 2 methods; namely by tabulating the Figure 1.1 or by way of equation. These are to be proven as below. Figure 1.1 shows the computation of each MPL and it clearly illustrates that MPL = 41 where it employs 1 unit of capital and 3 of labor. K = 1 unit | K = 2 units | K = 3 units | Quantity of Labor | Total Product | MPL | Quantity of Labor | Total Product | MPL | Quantity of Labor | Total Product | MPL | 1 | 100 | - | 1 | 123 | - | 1 | 139 | - | 2 | 152 | 52 | 2 | 187 | 64 | 2 | 193 | 54 | 3 | 193 | 41 | 3 | 237 | 50 | 3 | 263 | 70 | 4 | 215 | 22 | 4 | 263 | 26 | 4 | 319 | 56 | 5 | 233 | 18 | 5 | 286 | 23 | 5 | 366 | 47 | 6 | 249 | 16 | 6 | 306 | 20 | 6 | 407 | 41 | 7 | 263 | 14 | 7 | 323 | 17 | 7 | 410 | 3 | Equation 1.1 shows how MPL is computed. MPL = ∆Q / ∆L = (193 – 152) / (3 – 2) = 41 /1 = 41 MPK = ∆TP / ∆K = (193 – 0) /1 = 193 /1 =193 MRTSLK = MPL / MPK = 41 / 193 = 0.2124 Hence, MPL = 41, MPK = 193, MRTSLK = 0.2124. b. Suppose that the firm currently employs 2 units of capital. The price of capital is $4 per unit and the price of labor is $10 per unit. What is the short-run total cost of producing 263 units of output' What is the long-run total cost of producing 263 units of output' [3 marks] Short-run total cost of producing 263 units as below :- TC = wL + rK = $10 (4) + $4 (2) = $40 + $8 = $48 Long – run total cost of producing 263 units will depends whether cost can be reduced by reallocating resources via checking cost minimizing condition as below :- Compare MRTSLK = w/r MRTSLK = MPL / MPK = 26 / 48 = 0.5417 w/r = 10 / 4 = 2.5 It is hereby proven that MRTSLK < w/r, whereby this company is not minimizing cost. It should adopt more capital and less labor. If the company use 3 units of capital and 3 of labor to produce the same quantity of 263 units, it will be reduce to total cost of :- TC = $10 (3) + $4 (3) = $30 + $12 = $42 Hence, short-run total cost = $48 and long-run total cost = $42 for producing 263 units. c. Suppose that the price of capital increases to $20 per unit and the price of labor falls to $5 per unit. Now what is the long-run total cost of producing 263 units of output' [4 marks] Simulation is to be done as using 2 units of capital and 4 of labor. Short-run total cost of producing 263 units as below :- TC = wL + rK = $5 (4) + $20 (2) = $20 + $40 = $60 Long – run total cost of producing 263 units will depends whether cost can be reduced by reallocating resources via checking cost minimizing condition as below :- Compare MRTSLK = w/r MRTSLK = MPL / MPK = 26 / 48 = 0.5417 w/r = 5 / 20 = 0.25 It is hereby proven that MRTSLK > w/r. It should adopt more labor and less capital. If the company use 1 unit of capital and 7 of labor to produce the same quantity of 263 units, it will be reduce to total cost of :- TC = $5 (7) + $20 (1) = $35 + $20 = $55 Hence, long-run total cost = $55 for producing 263 units. d. Beginning with 1 unit of capital and 2 units of labor, does this production function exhibit increasing, constant or decreasing returns to scale' Which way does the long-run average cost curve slope' [4 marks] It is hereby prove by multiplying the above resources to prove whether the ratio of resources increased match with the ratio of total product output increase. To simulate, the resources are multiplied by 3 or increase of 300% with a absolute value of 3.0 as follow :- Capital = 1 X 3 Labour = 2 X 3 = 3 units = 6 units When resources or multiplied, the output is 407 units. Increase in output = (407 – 152) / 152 = 255 / 152 = 1.68 or 168% It is proven that the ratio of resources increase vs output increase is 3:1.68 or 300% > 168%. The increment in resources does not produce the same ratio/increment percentage against total product output. Figure 1.2 clearly show on the chart by plotting the unit of capital (axis-y) vs unit of labor (axis-x) to produce the total product. Figure 1.2 Hence, the function exhibit decreasing returns to scale and upward sloping for long-run average cost curve slope.