Question

clear writing please

1. Utility is given by U(x,y) = y + 10y, with marginal utilities MU, = y and MU, = x + 10. The price of x is P, and the price of y is Py. The consumer has income m. (a) Assume first that we have an interior solution. Solve for the demand for u. (b) Suppose now that m = 100. Since I must never be negative, what is the maximum price for good x for which this consumer would ever purchase any x? (C) Suppose Py = 20 and P = 20. Show that the interior solution from part a) does not apply anymore. (d) What is the solution for P, = 20 and P, = 20? (e) Assuming income remains at 100, draw the demand curve for x for all values of

Answer 1

(x,y) = xytoy u-u (m is the income of consumer Muy = x tlo optimatity Condition is as The follows: MRS= Mux - Px Muy Py xtlo =) YPy = P x + 10 Pe - (1) 28 Tx P x + Ypy = my General equation of L y = m-x Px Budget line Using equation ① & 0 (2) Px x + 10px = m-x Pc 2 P x + 10l = m 2 PX = m-lope Demand for x = 1 Demand fra produselor 12 Poc XZO

& Suppase m=100 X O The maximum price of x is calculated as follows, but x =0, m=100 too = 5 2 x - 100 = 10px =) TP x = 10 Suppase Py=20, Pe=20 ,m=100 Now check these value y = 100 - 10 X 206_100 – 200 loo 2x20 40 As xzo in part (a), So at Py=20, Px=2 & m=100 the interior Solution from parta does not apply anymore.

(d) Py = 20 & Pax c20 The consumer will purchase zero mit qx & Y= M = 100 -5 units So the required solution is (0,5) ce) x demand curte of is as follows: Assume m=100, The for all values af x= m - 5 2px x = 100.5 2 px values of x fix alternativele Changing the Price of X 20 Quantity ofX