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1.Neoclassical Model: (a) (2pts) Draw and fully label a production function graph for output and labor in manufacturing that exhibits the law of diminishing returns (LDR). (Use numerical values to demonstrate the LDR. However, use different numbers than I used in class.) (b) (2pts) Explain why increases in labor are subject to the LDR. (c) (2pts) Use the numerical values from part (a) to derive a labor demand curve assuming that the price of each unit of output is equal to $10. (d) (2pts) Create a nominal wage rate and use that rate to describe in words and show graphically how many units of labor employers will hire. (e) (2pts) Find the real wage rate from your numerical example and explain in words the meaning of the real wage rate. (f) (4pts) In your own words, explain how the LDR causes the Production Possibilities Frontier to have a concave shape.
2.Neoclassical Model (cont.): Assume that a country produces and consumes two goods, food and computers and is in equilibrium in autarky. It now finds that it can trade at international prices where (P food/P computers) on the world market is greater than (Pfood/P computers) in the domestic market. (a) (2pts) If this country decides to engage in international trade what good should it export and why? (b) (2pts) To what extent should it specialize in the production of the good to be exported? (c) (2pts) How and why would your answer to part (b) be different under the assumptions of the Classical Ricardian model? (d) (4pts) Draw a fully labeled graph showing the autarky equilibrium, the degree of specialization, the consumption possiblility frontier, the optimal consumption bundle, the utility gain from trading, and the quantity of exports and imports.
Expert Solution
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From both figures above and also from above table it is clear that there exists Law of Diminishing Returns to a factor. The production function [ X = f(L) ] shows LDR because the graph shows increase in total output at decreasing rate. The downward sloped MPPL also exhibits LDR.
(b)
Increase in labour are subjected to LDR due to the following factors.
1.Fixity of the Capital (K) : Fixity of the capital is the principal cause behind the law of diminishing returns. As more and more units of labour are combined with fixed capital, the latter gets excessively utilized. It suffers greater wear and tear and loses its efficiency. Hence, the diminishing returns.
2. Imperfect factor substitutability ; Factors of production are imperfect substitutes of each other. More and more of labour cannot be continuously used in place of capital. Accordingly, diminishing returns are bound to set in if only the labour factor is increased to increase output.
(C)
In neoclassical model the VMP is considered as the demand for labour (calculated in above table)
Therefore, VMPL curve is the demand curve of labour in Neoclassical model, depected below.
(D)
As we have created nominal wage rate as $60 shown in the above table. The equilibrium employment of labor units will be determined where the Nominal wage rate (w) is exactly equal to the value of marginal product of labor (VMPL ??????). From the table (in part a) and graph (in part c) it is clear that, w = VMPL when firm is employing 8 units of labour. This is shown in graph (in part c) at point E.
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