A. Kingsley consumes units of goods X and Y. He faces a market which prices X at $a/unit, and Y at $b/unit. His total budget is $60.

1) Write the budget equation that Kingsley faces.

2) Sketch the graph of Kingsley’s budget line for goods X and Y.

3) Write the equation of the budget line in slope-intercept form. Identify the slope.

4) Sketch the optimal bundle and the indifference curve. How would you prove algebraically that this is the optimal bundle?

B. Suppose Kingsley has a utility function U = 2xcyd

1) Find the marginal utility for goods 1 and 2.

2) Determine the marginal rate of substitution of good 1 for good 2.

3) Derive the demand function for Good X (Hint: Solve the MRS equation in terms of Y, then substitute into the budget equation; solve for X).

4) Using the same rationale from 3), derive the demand function for Good Y.

5) Determine the inverse demand function for Good X (rearrange the demand function – solve in terms of price).