How to deal with double integrals of lognormal distributed variables?

Hi, I am a new user of matlab and I am trying to solve a problem that includes the estimations of two simultaneous integrals oover a lognormal and normal distributed variables.

In my model I try to estimate a supply of a certain good called s.

• In the model the producers have "ed" units that can convert one to one into "s"
• this endowment "ed" is lognormal distributed with mu = 1, and sd = 0.2
• the parameter phi accounts for firms´ productivity and is normaly distributed with mu = 5 and sd = 2.
• each firm produces its "ed" unitis into "s" if their productivity is higher than a threshold (that depends on several parameters and also form "ed" itself)

With these information, the supply that I want to estimate is : S(p)= Integral in "ed" from -inf to +inf of the integral in "phi" from phi_threshold to +inf of ("ed" *dF(phi)*dG(ed); were F() and G() are the distibution functions.

I know how to solve this problem if the distribution of firms and phi were discrete instead of continuos. If the distribution of firms were discrete, the supply would be divided in two: 1) for each "ed" the supply is equal to the summ of ed of all the firms with productivity higher that phi_threshold 2) the summ of the previous value over all the possible value of ed.

Actually, I directly solve this for each firm to find out if they have a higher productivity (phi) than its threshold, and then sum the individual supply to found the market supply.

The problem is that a need to estimate it for a continuos distribution of firms and I do not have any idea of were to start.

I would be extremely grateful if you can help me to handle this problem.

Thanks!

David