Question 2

A consumer purchases two goods, food (x) and clothing (y).  He has the utility function U(X,Y) = XY, where X and Y denote amounts of X and Y consumed. Marginal utilities of X and Y are MU_x = y and MU_y = x.  The consumer’s income is $72 per week and that the price of y is P_y = $1 per unit and price of x is P_x1 = $9 per unit.  

1. What are his initial quantities of X and Y demanded?  Show arithmetically.

2. Draw a diagram below to show the consumer’s budget line, his indifference curve and equilibrium point. On the diagram label or indicate quantities consumed of x and y. Do not mess up the diagram.  You may want to practice drawing the diagram on a different paper first.  (Figure 4.6 on page 118 is a good model for this exercise).

c). Suppose price of x now falls to P_x2 = $4.00; income and price of y remain the same.  What quantities of X and Y will be consumed after the fall in price of x?  Show arithmetically.

d). On the same graph as in part b), show the consumer’s new budget line, new equilibrium point on a new indifference curve. On the diagram label the new quantity consumed of x. What will this quantity be?

     e). On the diagram draw the budget line corresponding to the new price of x and tangent to old indifference   

     curve.  (You are trying to separate the income and substitution effects). What will be consumption of x at this  

     tangency point?

     f). What are the price effect, income effect and the substitution effect on the diagram above?

     What are their numerical values of these effects?  

     

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The consumers initial quantities of X and Y demanded can be determined by equating the budget line equation with the utility function and solving for ... View the full answer