Question

ACE Problem 1 (25 marks) BI LET A consumer buys two goods, good X and a composite good Y. The utility function is given as ELLE DEMO U(X,Y) = XY + X. 1=$10 Px = $0.5 Where I is income level, Px is the price of good X EL ele 1) Find the optimal basket that maximizes utility and calculate its corresponding utility level.(5 marks) 2) Show your answer for Questions (1) on a graph. ( 5 marks) 3) Suppose a $0.5 per unit tax is imposed on good X and the consumer bears its entire burden. What is the new optimal basket that maximizes utility, and calculate its corresponding utility level.( 5 marks) 4) Does this utility function have a diminishing MRSyx? Why? ( 5 marks) 5) Does this utility function satisfy the law of diminishing MU? why? ( 5 marks) T PC ER ELUT MEGET

py = $1

Answer 1

due to tax imposition, utility falls.

CLASSMATE U=XY+X 1-10 x = 1/2 Date Page Y+1 MRS - 20/ax 20/27 Pelly /2/1 1: Y+1 12 + am 2Y Y+ + Y = 10 24.9 y .4.5 20 U= 60.5 utility function has x indreases MRs because as diminishing mRs falls x T.U 0 0 4.2 mux: MV = Y+1 X m.U. - Marginal utility is not diminishing. It is constant. - 23 3 9 3 4 12 3 : 1 P IPy = / Y+1 Tax : 0.5 X + Y: 101 Y+ + SY10 2Y9 Y 4.5 x 5.5 U= 30.25 Y +1

Equilibrium is when MRS = price ratio.

MRS is diminishing.