DEPARTMENT OF ECONOMICS , FINANCE AND ACCOUNTING
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See below for assignment questions.
Answer all questions and explain your answers. All questions are marked out of 100 and carry equal weight.
1.(a) Consider the production function EMBED Equation.3. Show that this production function exhibits constant returns to scale when the input bundle is (K,L) (10, 20).
K110L120K210L220K310L320K410L42080160320640
By increasing the inputs, L and K, by the multiplier 2, the output also increased by 2. Therefore, it can be said that there is a constant returns to scale.
(b) Suppose that the marginal rate of technical substitution of capital (K) for labour (L) is always 3 (in absolute value). If a firm cuts its use of capital by 4 units, how many more units of labour will it require in order to keep output constant At what input price ratio will a producer only use labour (assume that the per-unit prices of K and L are r and w, respectively)
(c) If a production function exhibits economies of scale, then there cannot be diminishing returns to a factor. State whether the above statement is true, false or uncertain and explain your answer.
False. By definition, economies of scale are factors that cause the average cost per unit to fall as scale is increased. On the other hand, diminishing returns to a factor is how themarginalproduction of afactor of productionstarts to progressively decrease as the factor is increased. Relying on the two definitions, it can be inferred that diminishing returns to a factor refers to the output of the factor, independent of the cost of the production incurred. Therefore, it can be concluded that there can be diminishing returns to a factor if a production function exhibits economies of scale.
2. Fishing in Galway Bay requires both labour and capital input. The total number of fish obtained per hour (q) is given by where L and K are the respective labour and capital inputs per hour.
What is the average product of labour What can be said about the average product of labour curve
The maximum point of the APL curve is the boundary between Stages I and II of the Production Function.
What is the marginal product of labour What can be said about the marginal product of labour curve How does the average product of labour compare to the marginal product Explain your answer.
The maximum point of MPL curve is the Point of Inflection of the Production Function.
The average product of labour is the output per unit of labour input, while the marginal product of labour is the change of the total product from expanding labour by one unit holding capital constant. This means that the average product of labour is the output produced for every unit of labour used. On the other hand, the marginal product of labour is the change of the total product for every additional unit of labour used, holding capital constant.
The elasticity of output with respect to labour input is defined as the percentage change in output due to a 1 change in labour input. Can this be related to the marginal and average products of labour What is the value of the elasticity of output with respect to labour input
Yes, the elasticity of output with respect to labour input can be related to the marginal and average products of labour. If the value of marginal cost is less than the value of average cost, the output elasticity is less than 1, therefore, there is economies of scale. On the other hand, if the value of marginal cost is greater than the value of average cost, the output elasticity is greater than 1, therefore, there are diseconomies of scale. The value of elasticity of output with respect to labour input for the given problem is 0.8, coming from 0.8 of the Cobb Douglas function on the given production function. This means that a 1 change in Labour will result to a 0.8 change in output.
3. A bakery produces cakes with the following production function where q is the amount of cakes. In the short run, the firms capital equipment is fixed at K 50. The per-unit rental rate of K is r 2, while the per-unit wage rate of L is w 5.
Calculate the firm s short-run total (STC), average (SAC) and marginal (SMC) cost curves.capital is fixed regardless of production
What is the firms STC if it produces 50 cakes
Suppose now that all inputs are variable. What input combination will minimise the cost of producing 50 cakes How does your answer compare to that in (b) Explain any difference.