Final answer:
To derive Lisa's demand curve for pizza given her utility function U=Z^0.5B^0.5, maximize utility with the budget constraint pZZ + pBB = Y. Using the Lagrange multiplier method, solve the Lagrangian to find the optimal quantities of Z and B, then express the demand for pizza Z in terms of the price of pizza pZ, price of burritos pB, and income Y.
Step-by-step explanation:
To derive Lisa's demand curve for pizza from her utility function U=Z^0.5B^0.5, we first need to maximize her utility subject to her budget constraint. Lisa's budget constraint is given by pZZ + pBB = Y, where pZ is the price of pizza, pB is the price of burritos, and Y is her income.
Using the method of Lagrange multipliers, we set up the Lagrangian L = Z^0.5B^0.5 + λ(Y - pZZ - pBB), and take the partial derivatives with respect to Z, B, and λ, setting them to zero to solve for the optimal quantities of Z and B.
After finding these quantities, we can then insert the price of pizza pZ and other values into the demand function to get Lisa's demand for pizza, which is dependent on the price of pizza, pZ, price of burritos, pB, and her income, Y. This will give us an equation in the form of Z = f(pZ, pB, Y), which is her demand curve for pizza.