Final -2014:
Q-1.
a. What is meant by production function? Write similarities and de-similarities between Utility function and Production function.
b. Define and draw the Total product curve (TPC), Average product curve (APC) and Marginal Product curve (MPC). Discuss the important characteristics of these curves.
c. Given the production function q = 12x1x2 - 3.6x12 -3.2x22
Determine average productivity (AP) and marginal productivity (MP) of X1. Show that MP and AP are equal at the maximum point of AP is such point exists.
Q-2.
a. Define Isoquant line, Isocost line and rate of technical substitution (RTS). Obtain the first and second order conditions for constrained cost minimization.
b. Given the production function q= x1x2, determine the optimum output for the total cost of 6000 Taka, given per unit price of X1 40 Taka, per unit price of X2 50 Taka and fixed cost of 1000 Taka.
c. Define Ridge Lines. How would you construct Ridge Lines? Explain why a rational entrepreneur will not choose input combination beyond Ridge Lines.
Q-3:
a. Define Cobb-Douglas production function (CDPF) indicating its economic significance. Discuss in brief the important characteristics of a CDPF.
b. Define Constant Elasticity Substitution (CES) production function. Is CDPF CES production function? Show that elasticity of substitution between two factors of production is unity.
c. "When the return to scale is constant, the marginal physical product of variable factors of input diminishes" - Explain with geometrical interpretation.
Q-4:
a. Define short run 'cost function' and 'cost curve'. Which factors are included in Entrepreneur's cost? Indicate the steps for determining the 'cost function' as a function of quantity produced.
b. Define Marginal Cost (MC), Average total Cost (ATC), Average Variable cost (AVC) and Average fixed cost (AFC). Show these cost curves graphically. What are the important characteristics of MC?
c. For the given production function q = 5x1α1 x2α2, where α1 >0, α2 >0.
Obtain average cost (AC) , marginal cost (MC). Draw the AC and MC curves for
i) α1 + α2 >1 ii) α1 + α2 =1, iii) α1 + α2 < 1.
Q-5:
a. Obtain the first and second order conditions for profit maximization. Describe its geometrical description.
b. Assume that an entrepreneur's short run total cost function is
C= q3 -10q2 - + 17q +66.
Determine the output level at which he maximizes profit if selling price p =5. Compute the output elasticity of cost at this output.
c. What role does fixed cost play in entrepreneur's decision making process?
Q-6:
a. Derive the function of Pareto Income distribution. Interpret its parameters. Find the mean and variance od Pareto distribution. Mention some of its application. Is this income distribution applicable to Bangladesh.
b. Explain curve of concentration. How will you construct Lorenz curve for a given income distribution? Derive Gini's concentration ratio for income distribution with reference to Lorenz curve.
to be continued......
Q-1.
a. What is meant by production function? Write similarities and de-similarities between Utility function and Production function.
b. Define and draw the Total product curve (TPC), Average product curve (APC) and Marginal Product curve (MPC). Discuss the important characteristics of these curves.
c. Given the production function q = 12x1x2 - 3.6x12 -3.2x22
Determine average productivity (AP) and marginal productivity (MP) of X1. Show that MP and AP are equal at the maximum point of AP is such point exists.
Q-2.
a. Define Isoquant line, Isocost line and rate of technical substitution (RTS). Obtain the first and second order conditions for constrained cost minimization.
b. Given the production function q= x1x2, determine the optimum output for the total cost of 6000 Taka, given per unit price of X1 40 Taka, per unit price of X2 50 Taka and fixed cost of 1000 Taka.
c. Define Ridge Lines. How would you construct Ridge Lines? Explain why a rational entrepreneur will not choose input combination beyond Ridge Lines.
Q-3:
a. Define Cobb-Douglas production function (CDPF) indicating its economic significance. Discuss in brief the important characteristics of a CDPF.
b. Define Constant Elasticity Substitution (CES) production function. Is CDPF CES production function? Show that elasticity of substitution between two factors of production is unity.
c. "When the return to scale is constant, the marginal physical product of variable factors of input diminishes" - Explain with geometrical interpretation.
Q-4:
a. Define short run 'cost function' and 'cost curve'. Which factors are included in Entrepreneur's cost? Indicate the steps for determining the 'cost function' as a function of quantity produced.
b. Define Marginal Cost (MC), Average total Cost (ATC), Average Variable cost (AVC) and Average fixed cost (AFC). Show these cost curves graphically. What are the important characteristics of MC?
c. For the given production function q = 5x1α1 x2α2, where α1 >0, α2 >0.
Obtain average cost (AC) , marginal cost (MC). Draw the AC and MC curves for
i) α1 + α2 >1 ii) α1 + α2 =1, iii) α1 + α2 < 1.
Q-5:
a. Obtain the first and second order conditions for profit maximization. Describe its geometrical description.
b. Assume that an entrepreneur's short run total cost function is
C= q3 -10q2 - + 17q +66.
Determine the output level at which he maximizes profit if selling price p =5. Compute the output elasticity of cost at this output.
c. What role does fixed cost play in entrepreneur's decision making process?
Q-6:
a. Derive the function of Pareto Income distribution. Interpret its parameters. Find the mean and variance od Pareto distribution. Mention some of its application. Is this income distribution applicable to Bangladesh.
b. Explain curve of concentration. How will you construct Lorenz curve for a given income distribution? Derive Gini's concentration ratio for income distribution with reference to Lorenz curve.
to be continued......
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