Question

In: Economics

Suppose a consumer has preferences represented by the utility function U(X,Y) = X2Y Suppose PY =...

Suppose a consumer has preferences represented by the utility function U(X,Y) = X2Y Suppose PY = 1, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values PX = 1, PX = 2, and PX = 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference curve that goes through that bundle. Make sure to label your graph carefully and accurately.

Expert Solution

We have the utility function as , and is 1, while income (I) is 300. It can be checked that the indifference curve (IC) is convex to origin and will have unique (one) solution, where the MRS (slope of IC) will be equal to the slope of budget constraint. The budget constraint is , ie , for price of x will be checked with different values. The budget constraint can be arranged as and , which is the slope of the budget line. The IC's slope, or marginal rate of substitution (MRS) can be found as or (taking utility constant) or or or .

The consumer equilibrium will be where the MRS is equal to the slope of budget line, ie or .

In case , the consumer equilibrium will be at or . Putting it in the budget line , we have or or . Also, for y=100, or .

In case , the consumer equilibrium will be at or or . Putting it in the budget line , we have or or . Also, for y=100, or .

In case , the consumer equilibrium will be at or . Putting it in the budget line , we have or or or . Also, for y=100, or .

One can draw the graph by putting these required equilibrium in the different budget lines and get the price consumption curve (PCC). The IC's and BL's number corresponds to the price of x.

Rahul Sunny answered 1 year ago

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