Answer to Question #303062 in Microeconomics for Lina

Question

1. Explain in words;

a) What the budget line is.

b) Suppose we have two goods. The price of good one is 10 and the price of good two

is 15. The income is 30. Construct a diagram, with the quantities on the X and Y

axes and draw a budget line in the diagram.

c) How do the prices and do income affects the shape of the graph? What happens if the

price of one good rises? What happens if income increases?

d) State marginal rate of transformation in words.

e) Calculate MRT in question (b).

2. Given utility (𝑥, 𝑦) = √𝑥

√𝑦

, Px = 2, Py = 5 and M = 400, find:

a) The demand equation for X and Y.

b) The utility maximizing levels of X and Y.

c) The maximum utility

d) The MRSx,y at the optimum level

Answer 1

$P_xX+P_yY= M$

$P_x(2.5Y)+P_yY=M$

$2.5P_xY+P_yY=M$

$Y(2.5P_x+ P_y)= M$

Y$^*= \frac{M}{2.5P_x+ P_y}$

$P_xX+P_y(0.4X)=M$

$P_xX+0.4P_yX=M$

$X(P_x+0.4 P_y)= M$

X$^*= \frac{M}{P_X+0.4P_y}$

b) Utility Maximizing quantities

From the budget line

2(2.5Y)+ 5Y= 400

10Y= 400

Y= 40

2X+ 0.4(5X)= 400

4X= 400

X= 100

d) Maximum utility

= 40+ 100= 140

e) MRS$_{xy}= \frac{Mu_x}{Mu_y}= \frac{Y}{X}$

$=\frac{40}{100}= 0.4$