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.
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