c) Suppose the price of milkshakes increases to $5. How many units of milkshake and sushiare in Collin’s new optimal consumption bundle?

Given that the price of milkshakes pm increases to $5, we need to solve Collin's utility maximization problem again with the new prices.

Step 1: Set up the new budget constraint The new budget constraint is 100 = 5m + 10s.

Step 2: Set up the Lagrangian function The Lagrangian function is given by L = 2√m + s + λ(100 - 5m - 10s).

Step 3: Take the first order conditions The first order conditions are obtained by taking the partial derivatives of the Lagrangian function with respect to m, s, and λ, and setting them equal to zero.

∂L/∂m = 1/√m - 5λ = 0 ∂L/∂s = 1 - 10λ = 0 ∂L/∂λ = 100 - 5m - 10s = 0

Step 4: Solve the first order conditions From the first two equations, we can derive the optimal ratio of m and s:

1/√m = 5λ 1 = 10λ => 5λ = 10λ => √m = 2 => m = 4

Substitute m = 4 into the budget constraint:

100 = 5*4 + 10s => 100 = 20 + 10s => 80 = 10s => s = 8

So, the new optimal consumption bundle (m*, s*) is given by:

m* = 4 s* = 8