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6.6: Exercises for Chapter 6
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- In a spreadsheet enter the values 1... 16 as the X column (col A), and in the adjoining column (B) compute the value of utility corresponding to each quantity of X. To do this use the 'SQRT' command. For example, the entry in cell B3 will be of the form '=SQRT(A3)'.
- In the third column enter the marginal utility (MU) associated with each value of X – the change in utility in going from one value of X to the next.
- Use the 'graph' tool to map the relationship between U and X.
- Use the graph tool to map the relationship between MU and X.
- Follow the same procedure as in the previous question – graph the utility function.
- Why is this utility function not consistent with our beliefs on utility?
- Plot the utility function U=2X, following the same procedure as in the previous questions.
- Next plot the marginal utility values in a graph. What do we notice about the behaviour of the MU?
- If the utility function is of the form U=6X–X2, plot the utility values for X values in the range , using either a spreadsheet or manual calculations.
- At how many units of X (beer) is the individual's utility maximized?
- At how many beers does the utility become negative?
- Draw the budget line, with cappuccinos on the vertical axis, and music on the horizontal axis, and compute the values of the intercepts.
- What is the slope of the budget constraint, and what is the opportunity cost of 1 cappuccino?
- Are the following combinations of goods in the affordable set: (4C and 9M), (6C and 2M), (3C and 15M)?
- Which combination(s) above lie inside the affordable set, and which lie on the boundary?
- First, draw a budget constraint, with gasoline on the horizontal axis.
- Suppose now that, in response to a gasoline shortage in the economy, the government imposes a ration on each individual that limits the purchase of gasoline to an amount less than the gasoline intercept of the budget constraint. Draw the new effective budget constraint.
- Draw in the resulting equilibria or tangencies and join up all of these points. You have just constructed a price-consumption curve for good X. Can you understand why the curve is so called?
- Now repeat part (a), but keep the price of X constant and permit the price of Y to vary. The resulting set of equilibrium points will form a price consumption curve for good Y.