Question

In: Economics

Given​ Barbara's estimated​ Cobb-Douglas utility​ function, ​U(q 1​, q 2​) = q 1^0.2 q 2^0.8​, for​...

Given​ Barbara's estimated​ Cobb-Douglas utility​ function, ​U(q 1​, q 2​) = q 1^0.2 q 2^0.8​, for​ CDs, q 1​, and​ DVDs, q 2​, derive her Engel curve for movie DVDs. Illustrate in a figure. Let p be the price of ​ DVDs, $1.00 be the price of​ CDs, and Y be income. ​Barbara's Engel curve for movie DVDs is

Y= ? (Please provide answer)

​(Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts.​E.g., a subscript can be created with the​ _ character.)

Solutions

Expert Solution

The utility function is given to be , and the budget constraint would be or . The marginal utility would be or or and or or . The optimal combination of goods would be where or or or or or .

Putting this in budget constraint, we have or or or . This is the Marshallian demand for q2, ie DVDs. Now, the Engel curve is the combination of income and quantity demanded for different incomes with a constant price. Hence, the Engel curve would be or .

The graph is as below.

Engel curve with different prices is shown in the graph.

Rahul Sunny answered 2 years ago
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