lQuestion 4 '1'] Marks [0.5, I15, 2, 5, 3] ?r consumer has the following utility function U [X1.><2]=><1[><s +4] Prices of the two gootls X1 and x2 respectively are rm and o: and the consumer has income m. We assume that all prices and income are strictly positive. Furthermore, throughout this question we assume that m a 4P2- (ajl ((1.5 marks) Find the consumer's MRS between the two gootls lie, marginal utility of><1 divided by marginal utility of 3:2]. (h) ((1.5 marks) Write clown the eguation forthe consumer's hudget line and the slope of the budget line where x1 is on the horizontal axis and X2 is on the vertical axis.

A)

Marginal rate of substitution between the two goods is (x2 + 4) / x1

B)

Equation for consumer's budget line is m = x1 * p1 + x2 * p2

The slope of budget line = - p1 / p2

Step-by-step explanation

A)
U = x1 (x2 + 4)

U = x1 * x2 + 4 * x1

U = x1 * x2 + 4 * x1

Differentiating the above utility function with respect to x1, to get marginal utility from good x1 (MUx1)

dU/dx1 = MUx1

MUx1 = x2 + 4

U = x1 * x2 + 4 * x1

Differentiating the above utility function with respect to x2, to get marginal utility from good x2 (MUx2)

dU/dx2 = MUx2

MUx2 = x1 

MRS = Marginal utility from good x1 / Marginal utility from good x2

MRS = MUx1 / MUx2

MRS = (x2 + 4) / x1

Marginal rate of substitution between the two goods is (x2 + 4) / x1

B)

Equation for consumer's budget line is m = x1 * p1 + x2 * p2

Where m = Consumer's income,

x1 = Quantity of good x1

p1 = Price of good x1

x2 = Quantity of good x2

p2 = Price of good x2

The slope of budget line = - Price of good on horizontal axis / Price of good on the vertical axis

The slope of budget line = - p1 / p2