Answer to Question #268318 in Microeconomics for Ahona

Question #268318

Suppose the production function of an economy is given by:


Y = A̅K3/4 L1/4


A. Prove the production function is a homogeneous and follows a constant returns to scale.


Interpret the nature of production function.



B. Create a table and find out what are the five equations and five unknowns based on table-


that is reported in your text (pp.).



C. Solve these equations to get the solution to the model. Put your solution in the form of a Table


and explain the hiring rule of labor and capital based on graph of factor market equilibrium.


D. Estimate for the output per person in the long-run. Show it graphically. Explain why it follows


diminishing returns to scale.


E. Estimate TFP in the long-run, and explain TFP growth is crucial to make differences among


countries in terms of per capita GDP.


F. Point out the limitation of this model to explain long-run economic growth.


1
Expert's answer
2021-11-21T16:53:02-0500

Given,

Demand curve of good Y:

"QY=10\u22125P_Y+P_X"

Where,

QY=Quantity of good Y

PY=Price of good Y

PX=Price of good X


PY=price of the good Y=K1

PX=price of the substitute good=K2


The following formulas will be used:

Price elasticity of demand "=\\frac{\u2202Q_Y}{\u2202P_Y}\u00d7\\frac{P_Y}{Q_Y}"

Cross−price elasticity of demand "=\\frac{\u2202Q_Y}{\u2202P_x}\u00d7\\frac{P_x}{Q_Y}"

Calculation of price elasticity of demand:

"\\frac{\u2202Q_Y}{\u2202P_Y}=\u22125"

Let us substitute the values of Pand Pin the demand function for quantity

 of good Y

"Q_Y=10\u22125\u00d71+2\\\\Q_Y=10\u22125+2\\\\Q_Y=7"

Price elasticity of demand"=-5\\times{1}{7}"

Price elasticity of demand=−0.71

Calculation of cross-price elasticity of demand:

"\\frac{\u2202Q_Y}{\u2202P_X}=1\\\\P_X=K2\\\\Q_Y=7"

Cross−price elasticity of demand"=1\\times \\frac{2}{7}"

Cross−price elasticity of demand=0.29

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