Matthew need eggs (E) and premixed ingredients (I) to produce cake. Every cake needs exactly two eggs and one package of ingredients. When he adds three eggs and one package of ingredients, he still produces only one cake. Similarly, when he has only two eggs, he cannot produce two cakes even though he has two packages of ingredients.

a. Draw the isoquants for cake production with E on horizontal axis and I on vertical axis.

b. Find a mathematical expression for the production function for cake. What is the elasticity of substitution ?

c. Suppose the price of an egg is $1 and a package of the premixed ingredient costs $2. Let I be the total amount of money that Matthew spends on eggs and the premixed ingredient. Derive an expression for the quantity of cake produced as a function of I.

Consider the production function . At point , the firm uses units of capital and units of labor. At point , along the same isoquant, the firm would only use 2 units of capital.

a. Calculate how much labor is required at point .

b. Calculate the elasticity of substitution between and . Does the production function exhibit a higher or lower elasticity of substitution than a Cobb-Douglas production function over this range of inputs?