Tutorial 1 4 August 2022 1. Distinguish between a production plan and a production possibility set. 2. In words, distinguish between an input requirement set V(y) and an isoquant fory. 3. Consider the input requirement set, V0!) in the gure below. x2 It a. Explain whether or not this input requirement set is non-convex; motivate your answer. b. Explain whether or not x1 and x2 are divisible inputs in the region indicated by a circle; motivate your answer. C. Suppose that a rm faces this input requirement set as a technological constraint to minimize its production cost. Determine how many of vector of optimal input quantity, (xl'. xz') exist for every input price vector, (w, w). NB! You should be able to answer similar questions for the other three input requirement sets that we did in class/ or to compare and contrast them in light of questions above. 4. Consider the following constant elasticity of substitution (CES) technology; 1 y = f (x1.x2)=(ax1\" Huh\" )3, where .0 E [0.1] ; a=b=l a. Derive marginal rate of technical substitution (MRTS) for this technology. b. Derive the elasticity of substitution (0') for this technology. c. Show using MRTS and a', that: i. when p -b 00 the CES production function represents the Leontief production function. ii. when p = 1 the CES production function represents a perfect substitutes/ linear technology; iii. when p = 0 the CBS production function represents the Cobb-Douglas technology. 5 Determine Returns to Scale for the following technologies: 1. y = f (x1. xz)=(ax1\" Hm")? y = f(x1.xz)=(x1+x2)%