# Question: carol consumes apples and cookies let xa r be the...

###### Question details

Carol consumes apples and cookies. Let *x _{a}*
∈R

_{+}be the amount of apples and

*x*∈R

_{c}_{+}be the amount of cookies. (R

_{+}=[0

*,*+∞) is the set of all positive real numbers). Her consumption bundle is denoted by (

*x*). Suppose

_{a},x_{c}*p*= 3 (price of one apple),

_{a}*p*= 2 (price of one cookie), and

_{c}*m*= 30 (income she can spend for her consumption).

Write down the equation for Carol’s budget line and draw it in a diagram. Determine the slope of the budget line. In the same diagram, shade the area of all consumptions bundles that Carol can afford (budget set).

Suppose now that government imposes a 50% value tax on cookies. Write down the new equation for Carol’s budget line. Determine the slope of the new budget line.

Suppose now that a local store gives a 50% discount on additional cookies if one buys 4 cookies. Draw Carol’s budget set.

Now assume that Carol only cares about the total amount goods she consumes (i.e., she does not care whether a good is apple or cookie). For example, she is indifferent between consuming (1, 1) and consuming (2, 0). Draw her indifference curves. What are the best consumptions bundles that Carol chooses to consume in each of the above three cases?

Find *x*^{∗} that maximizes the following
function:

*f*(*x*) = *x*(1 − *x*)^{2}

*g*(*x*)=*x*^{0.5}(3−2*x*)^{0.5}