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Unformatted text preview: York University - ECON2350 - V. Bardis Answers to Practice Set 2 1. See notes. 2. Letting b = 2 gives q = f ( L ) = a ( L- t ) 1 / 2 . Then Jerry’s marginal product is f ( L ) = 1 2 a ( L- t )- 1 / 2 Setting pf ( L ) = w gives Jerry’s ‘input demand’ L * = ap 2 w 2 + t Substituting L * in the production function gives q * = a ( L *- t ) 1 / 2 ⇒ q * = a 2 p 2 w Is the latter equation Jerry’s supply? Almost, but not exactly. A complete answer has to distinguish between the case where Jerry chooses how much to supply before he travels to the forest (‘long-run’) and after he has gone there (‘short-run’). The latter is the easier one to deal with. If Jerry has gone to the forest he has incurred the ‘travel cost’ wt . If he finds out while there that the price is p he will supply as many units as the above equation specifies. His profit will be π * = pq *- wL * = p a 2 p 2 w- w " ap 2 w 2 + t # = a 2 p 2 4 w- wt If instead he chooses to supply zero then his profit will be π (0) =- wt < π * . Clearly since he has already incurred the fixed cost wt he should not consider it when deciding how many units to supply. By leaving out the fixed cost we in effect use ‘variable profit’ or ‘producer surplus’ as a measure of Jerry’s welfare in the short run: PS = π + F so here PS = a 2 p 2 4 w . Since PS is positive for any positive p in this example, Jerry will always find it profitable to supply q * = a 2 p 2 w in the short run. The comparative statics here are straightforward: ∂q ∂a = 2 ap 2 w > 0, i.e., the more productive he is the more he will supply at any price (supply curve shifts down); ∂q ∂p = a 2 2 w > 0, i.e., higher price increases quantity supplied; and ∂q ∂w =- a 2 p 2 w 2 < 0, i.e., an increase in the wage will reduce supply (supply curve shifts up). Finally, a change in t affects only fixed costs and so it has no effect on the short-run supply ( t is nowhere to be seen in the short-run supply function, so that ∂q * ∂t = 0). If Jerry decides before he goes to the forest (a ‘long-run decision’) then he will go only if his profit is not negative, that is, π * = a 2 p 2 4 w- wt ≥ 1 The above holds if p ≥ 2 w √ t/a . (The difference from before is that Jerry has not incurred the fixed cost at the time of decision and so he takes into account.) Then his supply function is q * = a 2 p 2 w , if p ≥ p , if p < p where p = 2 w √ t/a is the minimum price required for Jerry to enter....
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- Fall '12
- Jerry suppies