Q.3   A utility function is given by the equation U = 120 x0.7 y0.3 where x is the number of hours spent playing golf and y is the hours spent playing cards per month. Calculate the values of x and y for which utility is maximised, subject to the constraint 21x + 3y = 180

If the total utilities for the fifth and sixth units of a good consumed are 98 and 115 respectively. The marginal utility for the sixth unit is:

Ann's utility function is U = q1q2/(q1 + q2). Solve for her optimal values of q1 and q2 as a function of p1, p2 and Y.

Please get correct

Find the optimal bundle using the following utility functions and budget constraints. 1. U(x,y)=lnx+yand2x+y=10 2. U(x,y)=3x+2yand3x+2y=24 3. U(a,z)=3a+2zand3a+6z=24 4. U(a,z)=a2z2 and4a+2z=485. U(x,z)=a2z3 and3a+2z=36

Fang likes playing badminton with her friends. Her utility function for playing badminton every week is given by       U(t) = 11t – 2t2, where t is measured in hours. They play on a badminton court, which they can rent per hour. Suppose the current price to play on the badminton court is £2.50 per hour. How many hours should Fang play if she wishes to maximise her utility? Explain what we mean by the principle of diminishing marginal utility. Does the principle apply in Fang’s case? Explain why. In a diagram with income in pound sterling on the horizontal axis and quantity on the vertical axis, show the relationship between Fang’s budget and the number of hours that would maximise her consumer surplus.

Greg has the following utility function: u = x0.47x953. He has an income of $52.00, and he faces these prices: (p₁. p₂) = (1.00, 3.00). Suppose that the price of x, increases by $1.00. Calculate the equivalent variation for this price change.