I was confused about the meaning of the problem yesterday. Now I know the meaning of it and I can understand why "screening by delivery date". Let (t1,p1) and (t2,p2) be the contract, (t1,p1) is for the high value buyer and (t2,p2) is for the low value buyer.The aim of the seller is to maximize the expected revenue which is πH*p1+πL*p2(we assume the seller is risk neutral). In order to sell (t1, ...
I was confused about the meaning of the problem yesterday. Now I know the meaning of it and I can understand why "screening by delivery date". Let (t1,p1) and (t2,p2) be the contract, (t1,p1) is for the high value buyer and (t2,p2) is for the low value buyer.The aim of the seller is to maximize the expected revenue which is πH*p1+πL*p2(we assume the seller is risk neutral). In order to sell (t1,p1) to high value buyer and (t2,p2) to low value buyer, the seller confronts four restrictions:(1)VH*δ^t1-p1>=0 (2) VL*δ^t2-p2>=0 (3)VH*δ^t1-p1>=VH*δ^t2-p2 (4)VL*δ^t2-p2>=VL*δ^
t1-p1. The first two constraints are participation constraints and the last two are incentive compatibility constraints. It's easy to proof that (1) holds if (2) and (3) holds and (1) is not binding.We can also proof (2) and (3) are binding.By (2) and (3),it's easy to find the optimal parameters which satisfy (4). I'm sure you can solve it.My calculation shows that the contract is dependent on the relation of πH and VL/VH.In each cases t1=0, p1=VH+(VL-VH)*δ^t2, p2=VL*δ^t2. But t2 is dependent on the relation of πH and VL/VH. If πH> VL/VH, t2=∞. If πH= VL/VH,t2 can be any non negative value.If πH< VL/VH, t2=0.The answer is for reference only and you don't need give the coins.
The contract is not difficult to find.But I wonder why the problem is called screening by delivery date.I think the screening instrument is still the price.