PROBLEM (7) A consumer with I dollars budget has the utility u(x,y) = x(y+1) over amounts of cake (x) and ice cream (y) she consumes. The prices are px, py respectively. (a) Derive her demand for cake (x), as a function of prices p., py and her budget I. (b) Looking at the demand function in (a), is cake a normal good or an inferior good? Are cake and ice cream complements or substitutes? (c) Calculate the (i) (own) price, (ii) income, (iii) cross-price elasticity of demand for cake at the point where I = 80, px=10, py=20..

2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current in come is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?

sketch a person’s indifference map and budget line for two goods, X on the horizontal axis and Y on the vertical axis. Mark the optimum consumption point. Now illustrate the following (you might need to draw a separate diagram for each):         (a)  A rise in the price of good X (a normal good), but no change in the price of good Y.         (b)  A shift in the person’s tastes from good Y to good X.           (c)  A fall in the person’s income and a fall in the price of good Y, with the result that the consumption of Y remains constant (but that of X falls).

6. A consumer has an expenditure function given by E = Ū(P+). When the consumer has an income of 100, it can reach a maximum utility of 20. The price of x increases by 3 and the consumer's income increases by 25. Are they better off or worse off than before the changes? Explain how you know. Full solution please